Electric signal transmission system



July 1 l, 1939.

J. COLLARD ELECTRIC SIGNAL TRANSMISSION SYSTEM Filed Feb. 16, 1938ANGULAR FREQUENCY? INVENTOR Patented July 11, 1939 ELECTRIC SIGNALTRANSMISSION SYSTEM John Collard, Hammersmith, London, England,

assignor to Electric & Musical Industries Limited, Hayes, Middlesex,England of Great Britain a corporation Application February 16, 1938,Serial No. 190,832

In Great Britain February 18, 1937 20 Claims.

This invention relates in general to wave transmission systems, but moreparticularly, though not exclusively, to electric signal transmissionsystems.

The properties of any wave transmission path in which in a specificfrequency range the constants are substantially smoothly distributed areknown when the complex propagation constant is determined for allfrequencies within the specified range, where (x is the attenuationconstant and [3 the phase constant and R, L, G and C are respectivelythe resistance, inductance, leakance and capacity of the transmissionline per unit length and w is the angular frequency of the signals beingtransmitted. If the attenuation constant 0: is independent of frequencythen all oscillations caused to travel over the path will do so withoutthe occurrence of variations in relative amplitude. If also the phaseconstant ,8 is proportional to to so that the time delay d6 HE isconstant, then relative phases will also be transmitted undisturbed.

In general, with a cable or transmission line, these conditions are notsatisfied and it is therefore necessary to employ equalising orcompensating circuits whereby the attenuation constant is madesubstantially independent of frequency and the phase constantsubstantially directly proportional to frequency over the frequencyrange of the signals transmitted along the transmission line or cable.The variation with frequency of the attenuation and phase of thetransmission line or cable arises either due to the variation withfrequency of the effective resistance and inductance of the cable or theeffective capacity and leakance of the cable or due to variation of allof these constants. In telephony, however, variations in phase arerelatively unimportant, so that the equalising circuits are providedmainly for the purpose of correcting the attenuation or losscharacteristic. Some effect on phase is always introduced by the use ofsuch circuits, but this is purely arbitrary so that if it is desired tocorrect for phase the addition of phase-correcting circuits isnecessary. If such phase-correcting circuits are used it may be foundthatthe loss will have to be corrected again, and so on. Such methods ofcorrection therefore are generally those of trial and error and thecompensation that is obtained is usually subject to random errors.

In transmitting a wide frequency range of sig- 7 nals along a cable,such as television signals which may extend from zero frequency up tosome megacycles per second, the problemis considerably more complex. Notonly are variations in amplitude particularly important, but relativephases in addition may be allowed to vary only within very small limits.In an actual high frequency cable, owing to the skin effect in theconductors, the resistance of the cable increases with frequency and theinductance falls. Further, owing tothe fact that the capacity of thecable acts not like an ideal condenser but like a somewhat complicatednetwork of condensers and resistances, the capacity tends to decreaseslightly and the leakance to rise as the frequency rises. With such acable it will be apparent that since all four primary constants willvary with frequency, the attenuation constant will vary with frequencyand the phase constant will not be proportional to frequency. Distortionof the signals transmitted along such cable both in amplitude and phasewill therefore result. The use of equalising and compensating means istherefore necessary to reduce the distortion. However, the use of themethods of correction previously referred to, which necessarily involvethe introduction of random effects, is of little value since the randomeffects may total to a magnitude of considerable extent, especially overa long length of cable.

The present invention is primarily concerned with the simultaneousequalisation of the attenuation and phase of a cable or transmissionline designed to handle a wide frequency band of signals, but as will beapparent hereinafter, the invention is capable of a much widerapplication.

In this specification and in the appended claims, what is meant byequalisation of attenuation and phase is that the attenuation constantis made substantially independent of frequency and the phase constant ismade substantially directly proportional to frequency over the range offrequencies for which equalisation is effected.

It is known that where oscillations, such as mechanical or acousticaloscillations, are required to be transmitted, similar difficulties areencountered due to the attenuation and phase of the transmission pathand it is also well known that the analogues of resistance, inductance,capacity and leakance exist in the mechanical and acoustical cases.

applicable to mechanical and acoustical transmission systems.

The object of the present invention is to provide an improvedtransmission system in which the variation of loss and phase due tovariation with frequency of the effective resistance and inductance orcapacity and leakance, or both, (or their analogues) is simultaneouslyequalised and in which the equalisation is effected with considerablyreduced random errors.

Various forms of equaliser sections for electrical signal transmissionlines have been proposed comprising combinations of inductance andcapacity or resistance arranged so as to produce the complement of thevariation of attenuation and phase introduced by a cable, but with suchequalisers it was necessary to equalise loss and phase separately.

The present invention can be employed with any suitable type ofequaliser section providing that the equaliser sections employed producesimilar characteristic curves such as can be expressed as a function ofwhere p is an angular frequency defined in the same way for all sectionsemployed and w is the angular frequency at which the property whosebehaviour characterised by the curves is evaluated. This implies thatthe zero frequency loss for all sections is the same. The frequency pwill hereinafter and in the appended claims be referred to as thereference frequency. In sections of the simple type comprising seriesarms composed of resistances shunted by condensers and shunt armscomposed of inductances in series with resistances a convenientreference frequency to take is that frequency at which the reactance ofeach arm becomes equal to its associated resistance. In more complicatedtypes in which several reactances and resistances may be employed thereference frequency may be taken as that at which some particularreactance becomes equal to some particular resistance. It will be foundthat the reference frequency will always correspond to a value at whichthe loss of the section has fallen to a certain fraction of its maximumvalue. The reference frequency may therefore be regarded as that angularfrequency at which the loss of the section has fallen to somearbitrarily chosen fraction of its maximum value, which fraction issubstantially constant for all sections. The present invention is basedupon the principle of arranging the equaliser sections in such a mannerthat their reference frequencies are spaced at values corresponding tosubstantially equal increments of variation of the transmission path. Byemploying such a principle it is possible to equalise a cable withoutthe introduction of serious random errors, provided, for example, thatthe loss curve of the path can be resolved into one or more componentcurves of the form Ana)", or that the phase curve of the path can beresolved into one or more component curves of the form Bnw"; moreover,if the cable is such that the type n B =A tan are satisfied, thensimultaneous equalisation of loss and phase delay is achieved.

In general the principle of equal spacing may be applied to equalisedistortion arising from any frequency characteristic which may beexpressed as a finite power series in frequency.

Accordingly, the present invention broadly comprises a wave transmissionsystem including a transmission path with substantially smoothlydistributed constants along which oscillations extending over a range offrequencies are caused to travel, and in which the path is such as tocause distortion of the oscillations which varies with the frequenciesof the respective oscillations owing to the variation with frequency ofthe effective resistance and inductance or the capacity and leakance, orboth (or their analogues), and in which the characteristic curve of thecable can be analysed into the form mentioned above and wherein acompensating or equalising path is associated with said transmissionpath comprising a plurality of equaliser sections the referencefrequencies of which are spaced at values corresponding substantially toequal increments of variation on the component curve or curves of thetransmission path, said sections being designed in such a manner, inconjunction with their spacing, as to produce substantially thecomplement of the increment of variation so that the loss and phasedistortion due to variation with frequency either of effectiveresistance and inductance or of capacity and leakance. or both,. aresimultaneously equalised.

More specifically, the invention is concerned with the case in which thepath is such as to cause attenuation and phase distortion of theoscillations and in which the reference frequencies of the equalisersections are located at frequencies corresponding substantially to equalincrements of loss of the component curve or curves of the transmissionpath and designed in such a manner that the loss of the transmissionpath is made substantially independent of frequency and the phaseconstant substantially directly proportional to frequency.

The present invention is especially applicable to an electric signaltransmission system which is designed for the transmission of signalsextending over a very wide frequency range extending at least up to 100kilocycles per second. The invention is also applicable to the case inwhich the transmission line is designed for the transmission offrequencies from substantially zero frequency up to about two or threemegacycles per second, such latter frequencies being ordinarilyencountered in the transmission of television signals. When dealing withsignals extending over such a wide range of frequencies the variation ofattenuation and phase is due to variation with frequency of all fourprimary constants of the cable and the present invention can accordinglybe applied to such a system for equalising simultaneously the greaterpart of the variation of the loss and phase. The invention may also beapplied to transmission lines or cables transmitting signals extendingover much smaller frequency ranges. It may also be employed in atransmission line or cable for equalising the effect only of variationwith frequency of the resistance and inductance or capacity andleakance. It is also possible to apply it to a cable in which theequalisation is effected by loading the cable at intervals along itslength, which intervals are short compared with the wavelength of thehighest frequency to be transmitted or to the case in which an arbitrarylength of cable or transmission line is equalised as a whole by the useof a. plurality of equaliser sections.

In all cases the reference frequencies of the equaliser sections will belocated at frequencies corresponding to equal increments in thevariation of the transmission path and, subject to certain conditionshereinafter to be referred to, any type of equaliser section may beemployed in the invention. The invention preferably employs equalisersections of the so;-cal.led constant resistance type but is not limitedin scope to the use of such sections.

In order that the said invention may be clearly understood and readilycarried into effect the same will now be more fully described withreference to the accompanying drawing in which:

Figure 1 illustrates the manner in which the loss of a cable, such asmight be employed for television purposes, varies in the range from zerofrequency to frequencies of several mega cycles per second,

Figures 2, 3 and 4 illustrate networks which may be employed in theinvention, and

Figure 5 illustrates an improved type of equaliser section according toa feature of the invention.

The invention will now be described more fully and as applied to atransmission line or cable in which variation of the four primaryconstants of the cable occurs With variation in frequency and in whichit is desired to equalise simultaneously the greater part of the lossand phase due to the variation of these four primary constants.

Figure 1 illustrates a typical loss curve of a cable. In order to avoida relative variation in the amplitude of signals at various frequenciestransmitted along a cable having such a-characteristic, it is necessary,as stated above, to employ an equaliser which may take the form ofloading at intervals along the length of the cable but moreconvem'entlythe equaliser is in the form of an artificial line inserted in serieswith the cable at a convenient point before or after suitableamplifiers. The equaliser is designed to produce the complement of theloss produced by the cable so that when the equaliser is connected tothe cable the overall loss is substantially constant over the frequencyrange for which the equaliser is designed. It has been found that anequaliser of the form described here which is designed to make theoverall loss of a cable substantially independent of frequencysimultaneously makes the phase constant directly proportional tofrequency.

The sections of an equaliser constructed in accordance with theinvention are arranged so that their reference frequencies, ashereinbefore defined, are spaced at values corresponding substantiallyto equal increments of loss of the cable. As shown in Figure 1, theangular frequency p1, 1122, etc., correspond to substantially equalincrements in loss of the cable characteristic. The equaliser designedin accordance with the invention has the reference frequencies of thesections arranged so that they are equal to 121, 2122, etc.

In the following explanation of the invention it will be shown how theproper spacing of the angular frequencies 111, 102, etc., may bedetermined. The equaliser sections employed produce similarcharacteristic curves as stated above, such as can be eXpressedby afunction of B Let) (q) where p being the reference frequency, be thevariable part of the loss at frequency w due to any one of a number oflike sections so that the variation of loss due to all the sectionsmaybe expressed as where a dash signifies a first differentiation, anddue to this number of sections there will be contributed an amount ofloss at a frequency w equal to The total loss at this frequency is,therefore,

i ;'"(p)f( d X 0 0) p The sections will accordingly possess the sametotal loss characteristic as the curve along which they have beendistributed if This can be shown' to lead to a finite value of :c ifF(w) is of the form Aw It is in fact then found directly that Turningnow to a consideration of the phase characteristic that will be obtainedwith this distribution let (q) represent the phase characteristic of anyone section. Performing an integration'in the same way as before thetotal phase at an angular frequency w willbe Subject, therefore, to, aconsideration of the finiteness of these integrals it appears that if inthe loss characteristic of a network constructed as herein supposedthere occurs a term ca in the loss characteristic, then there will alsooccur a term w in the phase characteristic. This is a completelyfundamental relation for all equalisers having sections possessingsimilar character curves and spaced as stated above, since it isindependent of the forms of f (q) and (q).

In order to determine the conditions of finiteness for the integralsiii) and

it is necessary to consider special cases, since such conditions willclearly depend on the special forms of f (q) and (q). The special caseof a constant resistance section will be selected for purposes ofillustration but it will be understood that the in-- vention is notlimited in its use to the constant resistance type of section.

It is necessary for this problem to determine the propagation constantas a function of q since the propagation constant has already beensupposed to possess a variable real part f(q) and an imaginary part (q).Now in a constant resistance section, by which is meant a sectionpossessing a series arm of impedance Z1 and a shunt arm of impedance Z2,such that Z1Z2=Zo and having an additional resistance Z0 connectedeither across the series arm or in series with the shunt arm, thecurrent ratio 70, as is well known, is given by In terms of k, thepropagation constant is simply given according to It is thereforenecessary to express Z2 as a function of q, and it has been foundpossible to do this in a very general manner by a process of building upany impedance from elementary impedances comprising either resistance inseries with inductance, resistance in parallel with inductance,resistance in series with capacity or resistance in parallel withcapacity. By this method it may to zero the value of the attenuationconstant tends to Zlog and that as w tends to infinity the attenuationtends to i. e., to

2 log g s Q( t cool so that if Q(t) Q(a) then the attenuation atinfinite frequency is greater than that at zero frequency. It Q(t) Q(a)then the attenuation at finite frequency is less than that at zerofrequency. Thus by adjusting the relative values of Q) and Q(a) it ispossible to give the attenuation curve of the section a general rise ora general fall over the whole frequency range from zero to infinity. Thecurve over any particular part of the frequency range, however, may riseor fall according to values of the individual terms (q +t and (q -l-a Inproceeding to consider the previously mentioned integrals it ispermissible to deal with each term in f(q) and (q) separately. Thuscorresponding to the general term in f(q) there is the integral 1. e.,to

p being a constant frequency as defined in any arbitrary way and asstated in the so-called reference frequency.

By virtue of this fact it is possible to write for k the very generalexpression 1(q+j 1) 2(q+j 2) i(q+j 1) 2(q+j 2) where s1, s2, etc'., andt1, t2, etc., are further real constants of the kind as referred toabove. For convenience this form will be contracted to:

Q( )Q(q+j Q( )Q(q+j by using the notation Q(z)=z1, 22, 23, It

follows directly from this form that q t2 1 +a (q)=2 tan" %-2 tan" Inpassing, and before proceeding to employ these derivations it may bepointed out that as w tends Now it can be shown that is finite providedb-I exceeds a. Applying this result to the first integral in theexpansion, since this term constitutes the greatest restriction on n, itfollows that n-I must be less than unity, and, therefore, that 11 mustbe less than two.

By a similar procedure it may be shown that is finite for all values of12 less than unity.

Also if n is less than unity it can be shown that 117i q"" (q) q 0 Forn= this becomes I17! COS T The following conclusions are therefore to bedrawn:

(a) If the power of w is two or over the spacing factor a: is infinite,so that in practice an equaliser of this type cannot be produced so asto possess a loss varying as a power of no equal or greater than two:

(b) If the power of w is equal or greater than unity the phase becomesinfinite at all frequenc1es:

(c) For powers of to less than unity a term Aw in the attenuation isaccompanied by a corresponding term in the phase.

Considering now the expression for f(q) it will be clear that for everyconstant resistance network obtained in the manner that has beendescribed above and having an attenuation component given by Anna thereis always a complementary network having a component equal to thenegative of this term, to be obtained by an interchange of therespective constants t1, t2, etc, and a1, a2, etc. Moreover, if thefirst network possesses a phase characteristic with a component Bnw thisinterchange produces a network with a component -Bnw Thus, by puttingthese two networks together in series the resultant loss will beconstant and there will be no phase distortion. If, therefore, the cablehas such characteristics that any variation of loss can be representedby a series of terms: A1w Azw and such that the variation of phase canbe represented by a corresponding series of terms:

it follows that it can be equalised by a structure of the type describedhere.

From the above it will be appreciated that by constructing an equaliserhaving the reference frequencies of its sections spaced at valuescorresponding to substantially equal increments of loss, the loss andphase distortion of a cable can be simultaneously equalised.

It is necessary now to consider the limitations that must be imposed onthe sections employed in the equaliser. It has already been stated thatthe loss of a single equaliser section must be small compared with theloss required to be equalised. Since the loss characteristic of a cableis one which rises with frequency it is clear that the characteristic ofa single section must fall with increasing frequency. Hence Q (a) mustexceed Q (t) and it follows that the impedance of the shunt arm musttend to a limit at infinite frequency which is larger than its value atzero frequency.

It follows that the impedance of the shunt arm must never be zero atfinite frequencies since otherwise infinite attenuation would result. Inparticular, it must not be zero at zero frequency.

The corresponding conditions for the series arm follows of course fromthe relation Z1 Z2=Z0 Having now indicated in some detail the nature ofthe methods by which variations in a transmission line may becompensated for, by showing how they may be employed to counteractvariations in total loss and phase it will now be shown how they may beapplied to equalis e directly variations in inductance and resistance orcapacity and leakance in a short length of line,

i. e., short compared with the shortest wavelength transmitted.

' It may be shown by experiment or by calculation that the variations ofresistance and inductance, which are the components introducing"distortion into the transmission, are represented with sufficientaccuracy for frequencies greater than 50,000 cycles per second by a termwt and mi respectively. Now a resistance varying like wt is provided bya chain of parallel connected resistance and inductance elements such asis shown in Figure 2. Thus, suppose the resistance elements are all thesame and of magnitude equal to R, then the impedance of any one elementin the chain is RjwL R+jwL from which it follows that the totaleffective resistance of the whole chain is the sum of all such terms as1 q where sip . p being that angular frequency at which the reactancebecomes equal to the resistance. Performing this summation it is foundthat any resistance variation like Aw may be obtained if thedistribution of elements is made by equal increments as in resistancewhere This spacing gives rise to a reactance term CXI , and. thereforeto an inductance term connected in series with a capacity C ifE=R1R2=ZD2 Thus it is possible to simulate the variations of resistanceand inductance by a number of suit-- ably distributed shunt elementsformed by capacities in series with resistances. As a furtherpossibility the same efiect may be obtained by a combination of the twotypes of simulating elements to give a network which possesses sectionshaving a characteristic impedance Z0. Such a network illustrated inFigure 4.

Since this network reproduces exactly the effect of the variations inresistance and inductance it follows that it reproduces exactly thevariations in loss and phase that occur in the cable due to thesevariations of resistance and inductance. Now the loss of a singlesection of this network is R; 1 ((1): VE +q so that the total loss at anangular frequency w of the network is Ace" w lR But the analysis givenearlier showed that such a loss characteristic could be provided by asuit? able distribution of any type of section subject only to certainlimitations. The cable may therefore be regarded merely an as infinitelyfinely distributed example of one of the types of structures discussedearlier. By the provision of a complementary structure it is thereforepossible to cancel the distortion that arises from variations ininductance and resistance. The effect of variations in capacity andleakage inductance may, using a similar argument, be shown capable ofelimination by the same general method.

In compensating for variations by any of the above methods it is notnecessary for the construction of an equalising network to be based onthe use of a single spacing factor x. It is possible to split up such anetwork into a plurality of subsidiary structures, each with its ownspacing factor provided a certain condition is satisfied by the spacingfactors x1, x2, of these subsidiary structures.

Thus, suppose sections possessing a characteristic f(q) are utilised,then by means of a spacing factor act; it is possible to'providea'characteristic A plurality of structures each with their ownparticular value of am; when connected in series are therefore capableof producing a characteristic expressed by nA at k w fq"" (q) q This maybe set equal to I The evaluation of spacing factors may be effected fromthe formula 93L x Z w 2 COS 7 where the (11, a2 etc., and t1, t2, etc.,are the constants that appear in the expression In deriving the aboveexpression for m it was found convenient to utilize an alternative inte-This may be obtained by calculating the total slope of the equalizercharacteristic at an angular frequency w and setting it equal to thenegative of the slope of cable at 0:.

When n It will be appreciated that so long as the loss and phase curvefor the cable or transmission line can be analyzed into the form statedabove, and providing the equalizer sections meet the requirementshereinbefore referred to, any suitable type of section may be employed.

It will thus be appreciated that there is a large number of equalizersections which are capable of equalizing simultaneously the loss andphase of a cable due to variation with frequency of the four primaryconstants of the cable and likewise there is a large number of equalizersections for equalizing either the resistance and inductance of a cableor the capacity and leakance of a cable when the cable has a lengthshort compared with the shortest wavelength transmitted. Any impedancewhich is suitable as a shunt arm for an equaliser for equalisingsimultaneously the loss and phase can be used as an element in a chainfor equalising leakance and capacity and any impedance suitable for useas a series arm for an equaliser for simultaneously equalising loss andphase can be employed as an element in a chain for equalising resistanceand inductance.

The equaliser sections for equalising simultaneously the loss and phasedue to variation with frequency of the four primary constants of thecable may be spaced at intervals along the length of the cable which areshort compared with the shortest wavelength to be transmitted or,alternatively, an arbitrary length of cable may be equalised as a wholeby a series of equaliser sections forming an artificial line disposed atany convenient point in the transmission system. The sections employedfor equalising the resistance and inductance or the capacity andleakance may be disposed as stated above at intervals along the lengthof the cable or where artificial line type of equaliser sections areused for equalising the variations of resistance and inductance orcapacity and leakance; such sections may be arranged as a whole at aconvenient point in an arbitrary length of cable.

The elementary type of equaliser section referred to above withreference to Fig. 4, i. e., one composed of a series arm consisting of acondenser C1 shunted by a resistance R1 and a shunt arm composed of aninductance L1 in series with a resistance R2 is termed an eightoctavetype, since it .is found that its loss changes substantially frommaximum to zero in about eight frequency octaves. The present inventioncontemplates the use of a modified form of section as shown in Figure 5,similar to the eight-octave type except that an additional condenser C2is inserted in shunt across the resistance R2 of the shunt arm and anadditional inductance L2 is inserted in series with the resistance R1 ofthe series arm, the resistance Z0 being equal to the characteristicimpedance of the section. With this modified form of section it is foundthat its loss falls from maximum to zero in only four octaves and,consequently, with the type of section shown in Figure 5 it is necessaryto locate the sections up to only about two instead of four octavesabove the highest frequency at which equalisation is required. With thefour-octave section, therefore, less sections are required with theconsequent reduction in dead loss produced by the equaliser and also areduction in the amount of amplification required.

It will be appreciated that the sections described above may be replacedby their electrical equivalents. For example, in the elementary type ofequaliser section composed of series and shunt arms the series arm. maycomprise a number of branches each formed by connecting a resistance inseries with a capacity, these branches being shunted by two resistancesin series whose joint is connected to the shunt arm, which comprises aresistance in series with a chain of parallel connected resistances andinductances.

In the practical application of the invention the characteristic curveof the cable to be equalised is first analysed either as a singlecomponent w" or a series of such terms, the number of terms depending onthe character of the curve. Over a large part of the range it may befound that 40 /2 fits the cable curve sufficiently well for practicalpurposes. The spacing factors appropriate to the values of n arecalculated from the above expression for a: substituting for a and t thevalues for the particular type of section being used. An equaliser foreach of the (o components is then constructed and these are thenassembled in series to form a complete equaliser of the artificial linetype or the sections of the equaliser are distributed along the lengthof the cable as stated above.

Any errors due to cable distortion which might arise at very lowfrequencies Where wL is no longer large compared with R may be correctedby any suitable means.

Although in the specific embodiment of the invention described anelectrical signal transmission system is referred to, it will beappreciated that the invention can also be applied to any Wavetransmission system in which similar difficulties are encountered due tothe attenuation and phase of the transmission path and in which the pathhas properties analagous to those of resistance, inductance, capacitanceand leakance. For example, in a long speaking tube for soundtransmission its loss and phasedistortion can be equalised in accordancewith the invention. The acoustical waves transmitted may be transformedinto their equivalent electrical oscillations by a suitable form ofmicrophone, the necessary equalisation being then effected by anelectrical equaliser.

It has also been suggested, in order to impart a time delay toelectricaljoscillations, to convert the cable, or line, into the form ofa power series,v

path.

the electrical oscillations into mechanical oscillations, as by applyingthe electrical oscillations to a piezo-electric crystal and to pass themechanical waves through a trough containing fluid and to re-convert themechanical waves trans-.

,mitted through the liquid into electrical oscilla after the mechanicaloscillations have been. re"

converted into electrical oscillations by employing an electricalequaliser of the kind hereinbefore described.

In the appended claims the quantities n, An

and B11 referred to therein are magnitudes determined by an analysis ofthe characteristics of the cable, or line, which is to be equalised.Thus an analysis is made of the loss characteristic of in the frequencyw, of which a typical term is" Amt". The index n is different for eachterm, and if only the loss is to be equalised, 11 may assume any valueless than 2; all that is necessary is that the sum of these power termsin w shall represent with some degree of accuracy the losscharacteristic of the line or cable. In the same way the phasecharacteristic may be, analysed into the sum of a number of power termsBnw".

Here, however, equalisation cannot be effected if.,

it is greater than unity. It will be appreciated therefore that if n isless than unity it may be possible to equalise both loss and phasesimultaneously; this can be effected if relations such as l'3,,=A tanhold between the coefficients An and BB, conditions found to hold truein practice.

I claim:

1. A wave transmission system including a n-lr A tan o)" said variationscausing distortions, and a compensating path associated with saidtransmission path comprising a number of groups, including one, ofequaliser sections, one group to every pair of said terms Aw" and n Atan o)" said sections of each group having attenuations at certainreference frequencies equal to their attenuation at zero frequencymultiplied by an arbitrary factor, said reference frequencies being sodistributed as to correspond to substantially equal increments in theassociated attenuation term, thereby substantially equalisingsimultaneously said distortion due to variations of attenuation andphase delay of said transmission 2. A wave' transmission systemincluding a transmission path along which oscillations extending over arange of frequencies are caused to travel and in which range owing tothe variation with frequency of the effective inductance and resistanceof said path the attenuation of said path varies with the frequency w asthe sum of a number, including one, of terms given substantially by Anw"and the phase delay of said path varies as'the sum of acorrespondingnumber, including one, of terms given substantially by Atan said variations causing distortions, and a compensating pathassociated with said transmission path comprising a number of groups,including one, of equaliser sections, one group to every pair of saidterms Arm" and 11 A tan ee" the sections of each said group havingattenuations at certain reference frequencies equal to their attenuationat zero frequency multiplied by an arbitrary factor, said referencefrequencies being so distributed as to correspond to substantially equalincrements in the associated attenuation term, thereby substantiallyequalising simultaneously said distortions due to variations ofattenuation and phase delay of said transmission path due to saidvariation with frequency of the effective inductance and resistance ofsaid path.

3. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range owing to the variation with frequency of theeffective capacity and leakance of said path the attenuation of saidpath varies with the frequency w as the sum of .a number, including one,of terms given substantially by Anw" and the phase delay of said pathvaries as the sum of a corresponding number, including one, of termsgiven substantially by I17! A tan o) said variations causingdistortions, and a compensating path associated with said transmissionpath comprising a number of groups, including one, of equalizersections, one group to every pair of said terms Auto and n A tan ev thesections of each said group having attenuations at certain referencefrequencies equal to their attenuation at zero frequency multiplied byan arbitrary factor, said reference frequencies being so distributed asto correspond to substantially equal increments in the associatedattenuation term, thereby substantially equalising simultaneously saiddistortions due to variations of attenuation and phase delay of saidtransmission pathdue to said variation with frequency of the effectivecapacity and leakance of said path.

4. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range owing to the variation with frequency of theeifective inductance, resistance, capacity and leakance of said path theattenuation of said path varies with the frequency w as the sum of anumber, including one,

of terms given substantially by Am" and the phase delay of said pathvaries as the sum of a corresponding number, including one, of termsgiven substantially by n'll' A tan a)" said variations causingdistortions, and a compensating path associated with said transmissionpath comprising a number of groups, including one, of equalisersections, one group to every pair of said terms Anw and the sections ofeach said group having attenuations at certain reference frequenciesequal to their attenuation at zero frequency multiplied by an arbitraryfactor, said reference frequencies being so distributed as to correspondto substantially equal increments in the associated attenuation term,thereby substantially equalising simultaneously said distortions due tovariations of attenuation and phase delay of said transmission path dueto said variations with frequency of the effective inductance,resistance, capacity and leakance of said path.

5. A wave transmission system including a transmission path along whichoscillations eX- tending over a range of frequencies are caused totravel and in which range the attenuation of said path varies with thefrequency w as the sum of a number, including one, of terms givensubstantially by Am", said variation causing distortion and acompensating path associated with said transmission path comprising anumber of groups, including one, of equaliser sections, one group toevery said term Anw", the section of each said group having attenuationat certain reference frequencies equal to their attenuation at zerofrequency multiplied by an arbitrary factor, these frequencies being sodistributed as to correspond to substantially equal increments in theassociated attenuation term, thereby substantially equalising saiddistortion due to variation of attenuation of said transmission path.

6. A wave transmission system including a transmission path along whichoscillations eX- tending over a range of frequencies are caused totravel and in which range owing to the variation with frequency of theeffective inductance and resistance of said path the attenuation of saidpath varies with the frequency w as the sum of a number, including one,of terms given substantially by Anw", said variation causing distortion,and a compensating path associated with said transmission pathcomprising a number of groups, including one, of equaliser sections, one

group to every said term Aw", the sections of each said group havingattenuations at certain reference frequencies equal to their attenuationat zero frequency multiplied by an arbitrary factor, said referencefrequencies being so distributed as to correspond to substantially equalincrements in the associated attenuation term, thereby substantiallyequalising simultaneously said distortion due to variation ofattenuation of said transmission path due to said variation withfrequency of the effective inductance and resistance of said path.

7. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range owing to the variation with frequency of theeffective capacity and leakance of said path the attenuation of ,60dueto variation' of phasedelay of said transmissaid path varies withthefrequency w' as the sum of a,number,- including one, of terms givensubstantially by Anni, said variation causing distortion, anda-compensating pathassociated with said transmission path comprising anumber of groups, ,including one, of equaliser sections, one group toevery, said term Anw", the sections of each said grouphavingattenuations at certain reference frequencies equal to theirattenuation; at zero freq encymultiplied by an arbitrary factor, Saidreferencefrequencies being so distributed as,,to correspond tosubstantially equal increments in the associated attenuation term,thereby substantially equalising said distortion ,du ento variation ofattenuation of said transmission path due to said variation withfrequency of the effective capacity and leakance of said path.

8. A wave transmission system including a transmissionpathalongwhichoscillations extending over. a range of frequencies arecaused to travel and in which range owing to the variationwithifrequency of the effective inductance, resistance, capacityiandleakance of said path the attenuation of said pathtvaries with thefrequency w as the sum of a number, including one, of terms givensubstantially by Anw", said variation causing distortion and acompensating path asSbiiiate'd withsaidtransmission path comprisirig anumb'erfof groupsin'cluding one, of equaliscr 'sectionsfone grouptoevery said term Ana), the sections ofeach group having attenuations atcertain reference frequencies equal to their attenuation at zero"frequency multiplied by an arbitrary -factor,said' referencefrequencies being'sddistributed as to correspond to substantially equalincrements in the associated attenuation"term thereby substantiallyequalising simultaneously saiddistortion due to variation of attenuationof said transmission path due to said variationwithfrequency of theeffective inductance, resistance, capacity and leakance of said path.-

9. A walvetransmission system including a transmission -path along whichoscillations extending over arange -offrequencies are caused to traveland in which range the phase delay of said path varies with thefrequency w as the ua-number, includingone, of terms givensubstantiallylby' its, said variation causing distor ashes compensatingpath associated with saidtransmission path comprising a number ofgroupsfincluding one, of equaliser sections, one group to every saidterm'Bnw, the sections of each said group having phase delays at certainreference frequencies equal to a single arbitrary value,saidreference'frequencies being so distributed'as to correspond tosubstantially equal increments in the associated phase delay term,thereby substantially equalising said distortion Sid I i path. p

"10. A wave transmission system including a transmission pathalong'which oscillations extending over a rangeof frequencies are causedto travel and inw'hich range owing to the variation with frequency ofthe effective inductance and resistance of said path the phase delay ofsaid path varies with the frequency w as the sum of a number, includingone, of terms given substantially by Bad)", said variation causingdistortion, and a compensating path associated with said transmissionpath comprising a number of groups, including one, of equalisersections, one group to every said term Bnw", the sections of each saidgroup having phase delays at certain reference frequencies equal to asingle arbitrary value, said reference frequencies being so distributedas to correspond to substantially equal increments in the associatedphase delay term, thereby substantially equalising said distortion dueto variation of phase delay of said transmission path due to saidvariation with frequency of the effective inductance and resistance ofsaid path.

11. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range owing to the variation with frequency of theeffective capacity and leakance of said path the phase delay of saidpath varies with the frequency w as the sum of a number, including one,of terms given substantially by Batu, said variation causing distortion,and a compensating path associated with said transmission pathcomprising a number of groups, including one, of equaliser sections, onegroup to every said term Bmu the sections of each said group havingphase delays at certain reference frequencies equal to a singlearbitrary value, said reference frequencies being so distributed as tocorrespond to substantially equal increments in the associated phasedelay term, thereby substantially equalising said distortion due tovariation of phase delay of said transmission path due to said variationwith frequency of the effective capacity and leakance of said path. 7

12. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range owing to the variation with frequency of theeffective inductance, resistance, capacity and leakance of said path thephase delay of said path varies with the frequency w as the sum of anumber, including one, of terms given substantially by Bnw", saidvariation causing distortion, and a compensating path associated withsaid transmission path comprising a number of groups, including one, ofequaliser sections, one group to every said term Bath), the sections ofeach said group having phase delays at certain reference frequenciesequal to a single arbitrary value, said reference frequencies being so.distributed as to correspond to substantially equal increments in theassociated phase delay term, thereby substantially equalisir g saiddistortion due to variation of phase delay of said transmission path dueto said variation with frequency of the effective inductance,resistance, capacity and leakance of said path.

13. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range the attenuation of said path varies with thefrequency w as the sum of a number of terms given substantially by AM",and a compensating path associated With said transmission pathcomprising a number, including one, but less than said number of terms,of groups of equaliser sections, each said group corresponding to asingle attenuation term given substantially by Aw", the sections of eachsaid. group having attenuations at certain reference frequencies equalto their attenuation at zero frequency multiplied by an arbitraryfactor, said reference frequencies being so distributed as to correspondto substantially equal increments in the associated attenuation term.

14. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range the phase delay of said path varies with thefrequency w as the sum of a number of terms given substantially by Bnw",.and a compensating path associated with said transmission pathcomprising a number, including one, but less than said number of terms,of groups of equaliser sections, each said group corresponding to asingle phase delay term.

' given substantially by Bnw, the sections of each said group havingphase delays at certain reference frequencies equal to a singlearbitrary value, said reference frequencies being so distributed as tocorrespond to substantially equal increments in the associated phasedelay term.

15. An electric Wave transmission system, particularly for television,including a transmission path as exemplified by a cable and atransmission line, along which path oscillations extending over a rangeof frequencies up to at least 100 kilocycles are caused to travel and inwhich range the attenuation of the path varies with the fre quency w asthe sum of a number, including one, of terms given substantially byAna!" and the phase delay of said path varies as the sum of acorresponding number, including one, of terms given substantially bysaid variations causing distortions, and a compensating path associatedwith said transmission path comprising a number of groups, includingone, of equaliser sections, one group to every such pair of said termsAW" and A tan n A tan w" the sections of each said group havingattenuations at certain reference frequencies equal to their attenuationat zero frequency multipled by an arbitary factor, said referencefrequencies being so distributed as to correspond to substantially equalincrements in the associated attenuation term, thereby substantiallyequalising simultaneously said distortions due to variations ofattenuation and phase delay of said transmission path.

16. An electric wave transmission system, particularly for television,including a transmission path as exemplified by a cable and atransmission line, along which path oscillations extending over a rangeof frequencies up to at least 100 kilocycles are caused to travel and inwhich range the attenuation of the path varies with the frequency w asthe sum of a number, including one,

of terms given substantially by Ana! and the phase delay of said pathvaries as, the sum of a corresponding number, including one, of termsgiven substantially by n A tan w fur A tan w" the sections of each saidgroup having attenuations at certain reference frequencies equal totheir attenuation at zero frequency multipled by an arbitrary factor,said reference frequencies being so distributed as to correspond tosubstantially equal increments in the associated attenua tion term,thereby substantially equalising simultaneously said. variations ofattenuation and, phase delay of said transmission path.

17. An electric wave transmission system, particularly for television,including a transmission path as examplified by a cable and atransmission line, along which path oscillations extending over a rangeof frequencies up to at least 100 kilocycles are caused to travel and inwhich range the attenuation of the path varies with the frequency w asthe sum of a. number, including one, of terms given substantially by Anwand the phase delay of said path varies as the sum of a correspondingnumber, including one, of terms given substantially by A tan %w" and acompensating path associated with said transmission path comprising anumber of groups, including one, of equaliser sections, arranged toconstitute an artificial line arranged: in series with said transmissionpath, one group to every such pair of said terms Ana" and the sectionsof each said group having attenuations at certain reference frequenciesequal to their attenuation at zero frequency multiplied by an arbitraryfactor, said reference frequencies being so distributed as to correspondto substantially equal increments in the associated attenuation term,thereby substantially equalising simultaneously said variations ofattenuation and phase delay of said transmission path.

18. A wave transmission system including a transmission path along whichoscillations extending over a range of frequencies are caused to traveland in which range the attenuation of said path varies with thefrequency w as the sum of a number, including one, of terms givensubstantially by Anw" and the phase delay of said path varies as the sumof a number, including one, of terms given substantially by A tan saidvariations causing distortion, and a compensating path associated withsaid transmission path comprising a number of groups, including one, ofequaliser sections, one group to every pair of said terms Ana! and A,tan 5w" said sections of. each group having attenuations at certainreference frequencies equal to their attenuation at zero frequencymultiplied by an arbitrary factor, said reference frequencies beingdistributed so as to correspond to substantially equal increments in theassociatedattenua tion term, said distortions due to variations ofattenuation and phase delay of said transmission path being therebysubstantially equalised simultaneously, said distribution being effectedusing an interval of loss equal to where f(q) is the loss characteristicof a single section and q equals 10 being said reference frequency of asection.

19. A wave transmission system including a transmission path alongwhich: oscillations extending over a range of frequencies on are causedto travel, said oscillations being thereby distorted according to afrequency characteristic expressible as a number, including one, ofterms of the form Xnw", and a compensating path comprising a number,including one, of groups of equaliser sections, each said groupcorresponding .to one said term, the sections of each said group havingfrequency characteristics of like nature to said frequencycharacteristic and possessing at certain frequencies a given arbitraryvalue, said latter frequencies being so distributed as to correspond toequal increments in the said corresponding term, the distortion of saidoscillations being thereby substantially reduced.

20. An electric wave transmission network for simulating a desiredfrequency characteristic as exemplified by that of a transmission line,a cable,=

and a complement thereof, said frequency char-* acteristic beingexpressible as a number, includ-- ing one, of terms of the form Xnw"which comprises a number, including one, of groups of electricalnetworks, each said group corresponding to one said term, the networksof each said group having frequency characteristics of like nature tosaid desired frequency characteristic and possessing at certainfrequencies a given arbitrary value, said latter frequencies being sodistributed as to correspond to equal increments in the saidcorresponding term, the networks being so designed to provide afrequency characteristic which substantially simulates said desiredcharacteristic.

JOHN COLLARD.

